Abstract
This chapter presents a discussion on scaling in the probability distribution of returns—the concept that has attracted significant attention from economists and physicists alike. There are two well-documented findings that motivate the further analysis of the financial time series. First, the probability distributions of returns often deviate significantly from the normal distribution because of fat tails and excess kurtosis. Secondly, returns exhibit volatility clustering. The latter effect has led to the development of the GARCH model. Early research of universality in the financial time series was based on the stable distributions. This approach, however, has fallen out of favor because the stable distributions have infinite volatility, which is unacceptable for many financial applications. The truncated Levy flights that satisfy the requirement for finite volatility are used as a way to solve this problem.
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